Finite Group Databasebeta

← #13124792

Subgroups — #13124792

Order 1664.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719510C211yesmaximal, characteristic
2#11719228C211yesmaximal, characteristic, complemented
3C13×#418C211yesmaximal, characteristic, complemented
4C2×#88072C211yesmaximal, characteristic, complemented
5#11718790C211yesmaximal, characteristic, complemented
6#11718782C211yesmaximal, characteristic, complemented
7#11718659C211yesmaximal, characteristic, complemented
8#11718445C212yesmaximal, complemented
9#11718440C212yesmaximal, complemented
10#11718438C212yesmaximal, complemented
11#11718435C212yesmaximal, complemented
12C22×D4×C13C2211yescharacteristic
13C2×#6127C2211yescharacteristic
14C2×C13×M16C2211yescharacteristic
15C13×#117C2211yescharacteristic
16#88207—22no—
17#88194—21no—
18#88192C2212yes—
19#88192C2212yes—
20#88190—21no—
21#88180C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C22×#1055C2211yescharacteristic
24#88146C2212yescomplemented
25C4⋊C4×D13C2212yescomplemented
26#88135—22no—
27C4×D52—21no—
28C4×Dic26—21no—
29C13×#102C2212yes—
30C13×#102C2212yes—
31#88072C2212yes—
32#88072C2212yes—
33#88060C2212yescomplemented
34#88060C2212yescomplemented
35#88058C2212yescomplemented
36#88057C2212yescomplemented
37#88048C2211yescharacteristic, complemented
38#88048C2211yescharacteristic, complemented
39#88047C2211yescharacteristic, complemented
40#88047C2211yescharacteristic, complemented
41C24×C13—21no—
42C2×D4×C13—21no—
43C2×D4×C13—22no—
44C2×D4×C13—22no—
45C2×D4×C13C2312yes—
46C22×C4×C13C2311yescharacteristic
47C2×C22⋊D13—22no—
48C2×C22⋊D13—22no—
49C2×C22⋊D13D412yes—
50C22×Dic13—21no—
51#6127—22no—
52#6127—22no—
53C2×D52D411yescharacteristic
54C2×C4×D13—22no—
55C2×C4×D13C2312yes—
56C2×Dic26D411yescharacteristic
57C13×M16—22no—
58C2×C8×C13C2312yes—
59C13×C4⋊C4C2311yescharacteristic
60C13×C4⋊C4C2311yescharacteristic
61C13×C22⋊C4—21no—
62C42×C13—21no—
63C22⋊Dic13—21no—
64C22⋊Dic13—22no—
65C22⋊Dic13—22no—
66#6103—22no—
67C4⋊Dic13—21no—
68C4⋊Dic13C2312yes—
69C4⋊Dic13C2311yescharacteristic
70C4⋊Dic13C2311yescharacteristic
71#6101—22no—
72C4×Dic13—21no—
73C4×Dic13—22no—
74C2×#1055—22no—
75C2×#1055C2311yescharacteristic
76C2×#1055C2311yescharacteristic
77#3096—131nomaximal, Sylow
78C23×C13—22no—
79C23×C13—42no—
80C23×C13—81no—
81C23×C13—81no—
82C23×C13C2×D411yescharacteristic
83C22×D13C2×D412yes—
84D4×C13—22no—
85D4×C13—22no—
86D4×C13—42no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13#4112yes—
91C2×C4×C13#4112yes—
92C2×C4×C13C2411yescharacteristic
93C22⋊D13—24no—
94C22⋊D13—82no—
95C22⋊D13—82no—
96C2×Dic13—22no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—81no—
100C2×Dic13C2×D412yes—
101D52—22no—
102C4×D13—22no—
103C4×D13—22no—
104C4×D13—82no—
105Dic26—22no—
106C8×C13—22no—
107#1055—21no—
108#1055—21no—
109#535—131no—
110#520—131no—
111#482—132no—
112#482—132no—
113#481—132no—
114#480—132no—
115#428—131no—
116#427—131no—
117#418D1311yescharacteristic, complemented
118C2×#102—131no—
119#408—131no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13—42no—
123C22×C13—42no—
124C22×C13—42no—
125C22×C13—84no—
126C22×C13#12312yes—
127C22×C13C22×D411yescharacteristic
128C2×D13—22no—
129C2×D13—22no—
130C2×D13—22no—
131C4×C13—41no—
132C4×C13—41no—
133C4×C13#12312yes—
134C4×C13C2×#4111yescharacteristic
135C4×C13C2×#4111yescharacteristic
136Dic13—22no—
137Dic13—42no—
138Dic13—41no—
139Dic13—41no—
140C2×#41—131no—
141C22×D4C2×D1311yescharacteristic
142C2×M16C2×D1311yescharacteristic
143C22×C8—131no—
144#127—261no—
145#124—261no—
146#121—132no—
147#121—132no—
148#120—262no—
149C4×Q8—261no—
150C4×D4—261no—
151C4×D4—262no—
152#117—131no—
153#117—132no—
154#117C2×D1311yescharacteristic
155C2×C4⋊C4—131no—
156C2×C4⋊C4—132no—
157#107—132no—
158#107—131no—
159#107—131no—
160#106—132no—
161#106—131no—
162#106—131no—
163#102—132no—
164#102—132no—
165#102C2×D1312yes—
166#102C2×D1312yes—
167C22⋊C8—132no—
168C22⋊C8—132no—
169C2×C13—22no—
170C2×C13—82no—
171C2×C13C2×#12311yescharacteristic
172C2×C13#57611yescharacteristic
173C2×C13#57711yescharacteristic
174D13—42no—
175C24—21no—
176#41—262no—
177#41—262no—
178C2×Q8—131no—
179C2×D4—22no—
180C2×D4—21no—
181C2×D4—22no—
182C2×D4—132no—
183C2×D4—131no—
184C2×D4—262no—
185C2×D4—262no—
186C2×D4C22×D1312yes—
187C22×C4—132no—
188C22×C4—262no—
189C22×C4—261no—
190C22×C4C22×D1311yescharacteristic
191M16—22no—
192C2×C8—131no—
193C2×C8—131no—
194C2×C8—262no—
195C2×C8C22×D1312yes—
196C4⋊C4—132no—
197C4⋊C4—131no—
198C4⋊C4—131no—
199C4⋊C4—262no—
200C4⋊C4—261no—
201C4⋊C4C22×D1311yescharacteristic
202C4⋊C4C22×D1311yescharacteristic
203C22⋊C4—21no—
204C22⋊C4—262no—
205C22⋊C4—262no—
206C22⋊C4—262no—
207C22⋊C4—261no—
208C42—21no—
209C42—262no—
210C42—261no—
211C13#309611yescharacteristic, complemented, Sylow
212C23—22no—
213C23—42no—
214C23—81no—
215C23—81no—
216C23—132no—
217C23D4×D1311yescharacteristic
218Q8—262no—
219D4—22no—
220D4—22no—
221D4—42no—
222D4—264no—
223D4—262no—
224D4—1042no—
225D4—1042no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—132no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—262no—
234C2×C4—1042no—
235C2×C4—1041no—
236C2×C4#612712yes—
237C2×C4D4×D1311yescharacteristic
238C2×C4#612912yes—
239C2×C4C23×D1311yescharacteristic
240C8—22no—
241C8—261no—
242C8—261no—
243C22—21no—
244C22—21no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—84no—
249C22—262no—
250C22—262no—
251C22—262no—
252C22#8813712yes—
253C22C2×D4×D1311yescharacteristic
254C4—41no—
255C4—41no—
256C4—262no—
257C4—522no—
258C4—521no—
259C4—521no—
260C4#8813712yes—
261C4C2×#612711yescharacteristic
262C4C2×#612911yescharacteristic
263C2—22no—
264C2—82no—
265C2—522no—
266C2C2×#8813711yescharacteristic
267C2#1171947911yescharacteristic
268C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#418C2
socleC22×C13C22×D4
prime radical#11719510C2
hypercenter#418D13
hypocenterC13#3096
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11719228C2semidirect
3. C13×#418C2semidirect
4. C2×#88072C2semidirect
5. #11718790C2semidirect
6. #11718782C2semidirect
7. #11718659C2semidirect
8. #11718445C2semidirect
9. #11718440C2semidirect
10. #11718438C2semidirect
11. #11718435C2semidirect
24. #88146C22semidirect
25. C4⋊C4×D13C22semidirect
33. #88060C22semidirect
34. #88060C22semidirect
35. #88058C22semidirect
36. #88057C22semidirect
37. #88048C22semidirect
38. #88048C22semidirect
39. #88047C22semidirect
40. #88047C22semidirect
117. #418D13semidirect
211. C13#3096semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117195102
#117192282
C13×#4182
C2×#880722
#117187902
#117187822
#117186592
#117184452
#117184402
#117184382
#117184352
#309613